An Optimization Approach to Generate Accurate and Efficient Lookup Tables for Engineering Applications

Abstract

In a wide number of engineering applications, the interpolation of a lookup table (LUT) can substitute expensive calculations. The generation of a LUT consists of pre-calculating a set of quantities from a collection of points that covers the study domain where the interpolation is possible. Nevertheless, the selection of points where the exact calculation is performed is of utmost importance for the LUT size and accuracy. Thus, the goal of this paper is to provide a dedicated optimization tool for the generation of accurate and efficient LUT. Here, the domain of the LUT is structured by the so-called layers, in which, the thicknesses of each layer define the distance between pre-calculated points. The optimization problem consists of maximizing the layer thicknesses, that is, minimizing the LUT size, such that the interpolation errors within the layer domain are kept under specified tolerances. Thus, a sequential design approach is applied to design each layer of the LUT until the layers cover the study domain. To achieve reliable LUT generations, a new optimization algorithm has been implemented to reach optimal layers with minimum iterations. The strategy proposed here is applied to generate a LUT to substitute a selected analytical function. The optimization procedures demonstrate not only the performance of the optimization algorithm, but also its convenience in the generation of multidimensional LUT.